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Simplifying 8100 + 195x + -1x2 = 0 Solving 8100 + 195x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8100 + -195x + x2 = 0 Move the constant term to the right: Add '8100' to each side of the equation. -8100 + -195x + 8100 + x2 = 0 + 8100 Reorder the terms: -8100 + 8100 + -195x + x2 = 0 + 8100 Combine like terms: -8100 + 8100 = 0 0 + -195x + x2 = 0 + 8100 -195x + x2 = 0 + 8100 Combine like terms: 0 + 8100 = 8100 -195x + x2 = 8100 The x term is -195x. Take half its coefficient (-97.5). Square it (9506.25) and add it to both sides. Add '9506.25' to each side of the equation. -195x + 9506.25 + x2 = 8100 + 9506.25 Reorder the terms: 9506.25 + -195x + x2 = 8100 + 9506.25 Combine like terms: 8100 + 9506.25 = 17606.25 9506.25 + -195x + x2 = 17606.25 Factor a perfect square on the left side: (x + -97.5)(x + -97.5) = 17606.25 Calculate the square root of the right side: 132.688545097 Break this problem into two subproblems by setting (x + -97.5) equal to 132.688545097 and -132.688545097.Subproblem 1
x + -97.5 = 132.688545097 Simplifying x + -97.5 = 132.688545097 Reorder the terms: -97.5 + x = 132.688545097 Solving -97.5 + x = 132.688545097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.5' to each side of the equation. -97.5 + 97.5 + x = 132.688545097 + 97.5 Combine like terms: -97.5 + 97.5 = 0.0 0.0 + x = 132.688545097 + 97.5 x = 132.688545097 + 97.5 Combine like terms: 132.688545097 + 97.5 = 230.188545097 x = 230.188545097 Simplifying x = 230.188545097Subproblem 2
x + -97.5 = -132.688545097 Simplifying x + -97.5 = -132.688545097 Reorder the terms: -97.5 + x = -132.688545097 Solving -97.5 + x = -132.688545097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '97.5' to each side of the equation. -97.5 + 97.5 + x = -132.688545097 + 97.5 Combine like terms: -97.5 + 97.5 = 0.0 0.0 + x = -132.688545097 + 97.5 x = -132.688545097 + 97.5 Combine like terms: -132.688545097 + 97.5 = -35.188545097 x = -35.188545097 Simplifying x = -35.188545097Solution
The solution to the problem is based on the solutions from the subproblems. x = {230.188545097, -35.188545097}
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